Reddit mentions of Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)

When I've got a clear aim in view for where I want to get to with a self-study project, I tend to work backwards.

Now, I don't know quantum mechanics, but here's how I might approach it if I decided I was going to learn (which, BTW, I'd love to get to one day):

First choose the book you'd like to read. For the sake of argument, say you've picked Griffiths, Introduction to Quantum Mechanics.

Now have a look at the preface / introduction and see if the author says what they assume of their readers. This often happens in university-level maths books. Griffiths says this:

> The reader must be familiar with the rudiments of linear algebra (as summarized in the Appendix), complex numbers, and calculus up to partial derivatives; some acquaintance with Fourier analysis and the Dirac delta function would help. Elementary classical mechanics is essential, of course, and a little electrodynamics would be useful in places.

So now you have a list of things you need to know. Assuming you don't know any of them, the next step would be to find out what are the standard "first course" textbooks on these subjects: examples might be Poole's Linear Algebra: A Modern Introduction and Stewart's Calculus: Early Transcendentals (though Griffiths tells us we don't need all of it, just "up to partial derivatives"). There are lots of books on classical mechanics; for self-study I would pick a modern textbook with lots of examples, pictures and exercises with solutions.

We also need something on "complex numbers", but Griffiths is a bit vague on what's required; if I didn't know what a complex number is than I'd be inclined to look at some basic material on them in the web rather than diving into a 500-page complex analysis book right away.

There's a lot to work on here, but it fits together into a "programme" that you can probably carry through in about 6 months with a bit of determination, maybe even less. Then take a run at Griffiths and see how tough it is; probably you'll get into difficulties and have to go away and read something else, but probably by this stage you'll be able to figure out what to read for yourself (or come back here and ask!).

With some projects you may have to do "another level" of background reading (e.g., you might need to read a precalculus book if the opening chapters of Stewart were incomprehensible). That's OK, just organise everything in dependency order and you should be fine.

I'll repeat my caveat: I don't know QM, and don't know whether Griffiths is a good book to use. This is just intended as an example of one way of working.

[EDIT: A trap for the unwary: authors don't always mention everything you need to know to read their book. For example, on p.2 Griffiths talks about the Schrodinger wave equation as a probability distribution. If you'd literally never seen continuous probability before, that's where you'd run aground even though he doesn't mention that in the preface.

But like I say, once you've taken care of the definite prerequisites you take a run at it, fall somewhere, pick yourself up and go away to fill in whatever caused a problem. Also, having more than one book on the subject is often valuable, because one author's explanation might be completely baffling to you whereas another puts it a different way that "clicks".]

These are listed in the order I'd recommend reading them. Also, I've purposely recommended older editions since they're much cheaper and still as good as newer ones. If you want the latest edition of some book, you can search for that and get it.

The Humongous Book of Basic Math and Pre-Algebra Problems https://www.amazon.com/dp/1615640835/ref=cm_sw_r_cp_api_pHZdzbHARBT0A


Intermediate Algebra https://www.amazon.com/dp/0072934735/ref=cm_sw_r_cp_api_UIZdzbVD73KC9


College Algebra https://www.amazon.com/dp/0618643109/ref=cm_sw_r_cp_api_hKZdzb3TPRPH9


Trigonometry (2nd Edition) https://www.amazon.com/dp/032135690X/ref=cm_sw_r_cp_api_eLZdzbXGVGY6P


Reading this whole book from beginning to end will cover calculus 1, 2, and 3.
Calculus: Early Transcendental Functions https://www.amazon.com/dp/0073229733/ref=cm_sw_r_cp_api_PLZdzbW28XVBW

You can do LinAlg concurrently with calculus.
Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) https://www.amazon.com/dp/0538735457/ref=cm_sw_r_cp_api_dNZdzb7TPVBJJ

You can do this after calculus. Or you can also get a book that's specific to statistics (be sure to get the one requiring calc, as some are made for non-science/eng students and are pretty basic) and then another book specific to probability. This one combines the two.
Probability and Statistics for Engineering and the Sciences https://www.amazon.com/dp/1305251806/ref=cm_sw_r_cp_api_QXZdzb1J095Y1


Differential Equations with Boundary-Value Problems, 8th Edition https://www.amazon.com/dp/1111827060/ref=cm_sw_r_cp_api_sSZdzbDKD0TQ9



After doing all of the above, you'd have the equivalent most engineering majors have to take. You can go further by exploring partial diff EQs, real analysis (which is usually required by math majors for more advanced topics), and an intro to higher math which usually includes logic, set theory, and abstract algebra.

If you want to get into higher math topics you can use this fantastic book on the topic:

This book is also available for free online, but since you won't have internet here's the hard copy.
Book of Proof https://www.amazon.com/dp/0989472108/ref=cm_sw_r_cp_api_MUZdzbP64AWEW

From there you can go on to number theory, combinatorics, graph theory, numerical analysis, higher geometries, algorithms, more in depth in modern algebra, topology and so on. Good luck!